In the field of seismic exploration, the earth interior is explored by emitting low-frequency, generally from 0 Hz to 200 Hz, acoustic waves generated by seismic sources. Refractions or reflections of the emitted waves by features in subsurface are recorded by seismic receivers. The receiver recordings are digitized for processing. The processing of the digitized seismic data is an evolved technology including various sub-processes such as noise removal and corrections to determine the location and geometry of the features which perturbed the emitted wave to cause reflection or refraction. The result of the processing is an acoustic map of the earth interior, which in turn can be exploited to identify for example hydrocarbon reservoirs or monitor changes in such reservoirs.
Seismic surveys are performed on land, in transition zones and in a marine environment. In the marine environment, surveys include sources and receiver cables (streamers) towed in the body of water and ocean bottom surveys in which at least one of sources or receivers are located at the seafloor. Seismic sources and/or receivers can also be placed into boreholes.
The known seismic sources include impulse sources, such as explosives and airguns, and vibratory sources which emit waves with a more controllable amplitude and frequency spectrum. The existing receivers fall broadly speaking into two categories termed “geophones” and “hydrophones”, respectively. Hydrophones record pressure changes, whereas geophones are responsive to particle velocity or acceleration. Geophones can recorded waves in up to three spatial directions and are accordingly referred to as 1C, 2C or 3C sensors. A 4C seismic sensor would be a combination of a 3C geophone with a hydrophone. Both types of receivers can be deployed as cables with the cable providing a structure for mounting receivers and signal transmission to a base station.
The spatial distribution of source and receiver locations in a seismic survey is referred to as layout or spread. A variety of spreads are known. Among those are spreads where receiver lines, a one-dimensional array of receiver locations, and source lines, the corresponding array of source or shot locations, are laid out at an angle. For the purpose of this invention, such layouts are referred to as “cross-line” geometry or acquisition. Such acquisitions have been described for example by G.L.O Vermeer, in “3D Symmetric Samplings”, 64th Ann. Internat. Mtg: Soc. of Expl. Geophys. (1994), 906-909 and later in the U.S. Pat. No. 6,026,058.
Seismic energy acquired at a receiver may contain upwardly and/or downwardly propagating seismic energy depending on the location of the receiver and on the event. For example seismic energy when it is incident (travelling upwardly) on the water-seabed interface, be partly transmitted into the water column and partially reflected back into the seabed. Thus, a seismic event will consist purely of upwardly propagating seismic energy above the seafloor, but will contain both upwardly and downwardly propagating seismic energy below the seafloor. As another example, seismic energy when incident on the water-air interface at sea level will be reflected back into the water column generating so-called “ghost” events. It is therefore often of interest to decompose the seismic data acquired at the receiver into an up-going constituent and a down-going constituent.
Various filters that enable decomposition of seismic data into up-going and down-going constituents have been proposed. For example in “Application of Two-Step Decomposition to Multi-Component Ocean-Bottom Data: Theory and Case Study”, J. Seism. Expl. Vol. 8, 261-278 (1999), K. M. Schalkwijk et al have suggested that the down-going and up-going constituents of the pressure just above the seafloor may be expressed as:
                                                        P              -                        ⁡                          (                              f                ,                                  k                  x                                ,                                  k                  y                                            )                                =                                                    1                2                            ⁢                              P                ⁡                                  (                                      f                    ,                                          k                      x                                        ,                                          k                      y                                                        )                                                      -                                          ρ                                  2                  ⁢                                                                          ⁢                                      q                    ⁡                                          (                                              f                        ,                        k                                            )                                                                                  ⁢                                                v                  z                                ⁡                                  (                                      f                    ,                                          k                      x                                        ,                                          k                      y                                                        )                                                                    ,                                  ⁢                                            P              +                        ⁡                          (                              f                ,                                  k                  x                                ,                                  k                  y                                            )                                =                                                    1                2                            ⁢                              P                ⁡                                  (                                      f                    ,                                          k                      x                                        ,                                          k                      y                                                        )                                                      +                                          ρ                                  2                  ⁢                                                                          ⁢                                      q                    ⁡                                          (                                              f                        ,                                                  k                          x                                                ,                                                  k                          y                                                                    )                                                                                  ⁢                                                v                  z                                ⁡                                  (                                      f                    ,                                          k                      x                                        ,                                          k                      y                                                        )                                                                    ,                            [        1        ]            where P is the pressure acquired at the receiver, P− is the up-going constituent of the pressure above the seafloor, P+ is the down-going constituent of the pressure above the seafloor, f is the frequency, kx, ky are the horizontal wavenumbers, vz is the vertical particle velocity component acquired at the receiver, ρ is the density of the water, and q is the vertical slowness in the water layer.
As can be seen, the expressions in equation [1] require two of the components of seismic data recorded at the receiver to be combined. These expressions are examples of combining two components of the acquired seismic data. It may also be necessary to combine two or more components of the acquired seismic data in order to decompose the acquired seismic data into P-wave and S-wave components, or to remove water level multiple events from the seismic data.
Further separation methods including free-surface multiple removal above the seafloor, wavefield decomposition into up- and downgoing constituents or P/S events above and below the surface, the splitting of particle velocities and traction are described in a number of published documents.
In U.S. Pat. No. 6,101,408, the ocean bottom wavefield separation described in three dimensions using an analytical solution. However, for practical applications, the filter is reduced to one dimension. A number of decomposition equations for various separations are developed by Amundsen et al. in the above cited U.S. Pat. No. 6,101,408 and in: “Multiple attenuation and P/S splitting of multicomponent OBC data at a heterogeneous sea floor”, Wave Motion 32 (2000), 67-78. A further review of decomposition methods for use in connection with the present invention is presented by L. Amundsen in: “Elimination of free-surface related multiples without need of the source wavelet”, Geophysics, Vol. 66, No. 1 (Jan-Feb 2001), 327-341.
Approximated compact spatial filters are further described by Osen et al. in: Towards Optimal Spatial Filters for Multiple Attenuation and P/S-Splitting of OBC Data”, EAGE 60th conference, Leipzig, Germany, 8-12 Jun. 1998, 1-29 Geophysical Division. A short length filter is obtained in terms of powers of kx using a series expansion.
When applying three-dimensional (3D) wavefield decomposition methods to data acquired in a cross-line geometry and sorted into 1-fold bins of common mid-points (CMPs) distributed evenly in a finely spaced “carpet” determined by in-line source and receiver spacings as proposed by Vermeer, it was noted that the known filter introduce an unacceptable level of noise due to sensor variations, statics and other perturbations.
In the light of the above prior art, it is seen as an object of the present invention to provide filters applicable to cross-line acquisitions or data collected through cross-line acquisitions and methods of applying such filters.